DeltaCE

The calculus of change, shown step by step, on your TI-84 Plus CE.
Type math the way it looks. Get exact answers the way your textbook writes them, and the steps behind them.

DeltaCE is a computer algebra system for the TI-84 Plus CE, built for algebra and Calc 1 to 3: exact answers (π²/6, not 1.64493), the steps behind them, graphs, statistics and more. A fork of FlowCE (itself a fork of KhiCAS).

Install it from the DeltaCE page: plug in the calculator, click Install, then press enter once on the calculator.

New in 2.3.2

± answers, factored, quadratic in form	Steps for many more equations
A matrix's picture	Distance, rate and time, with units

• Δ after an answer reads the equation: prgm after solving shows the equation's card (it said "No solution" for any equation with two answers or more).
• ± answers, as textbooks write them: x = −3 ± √13, x = (1 ± √5)/2, x = ±3, x = −1 ± 2i, in the console and on the card (the decimal form is still a ◀ ▶ away).
• Polynomial equations say more: factored over the rationals, how many solutions, and a quartic quadratic in form gets its substitution (u = x² + 6x), its equation in u and u's values.
• Steps for many more equations, and the steps button only where they come: quartics quadratic in form, polynomials that factor, |A| = |B|, 4ˣ with 2ˣ. (It promised steps for some and showed "No steps" after 15 s.)
• Word problems: distance, rate and time with units (minutes and hours mixed: 30 min at 60 mi/h is 30 mi); "how long to go", "how far at", "the speed to go"; every "find" answered in words; a negative width never chosen; the % now shows in the percent phrases.
• Pictures: larger, with visible axes and labels clear of the lines; a 2×2 matrix's unit square and its columns; a polynomial's sketch zoomed to where it turns.
• Editing: backspace undoes a list in a word problem's box, one item at a time.
• Checked against 121 real textbook word problems (OpenStax Elementary Algebra 2e): all right.
• Room for this: Laplace and Fourier transforms and a few college-level commands (lu, ker, resultant, ichinrem...) are out. Everything through AP Calculus BC stays, desolve included.

New in 2.3

Pictures on every Δ card	Systems drawn too
Factor trees, fraction bars, box plots	Answers in words, with units

• Every Δ card draws its picture: a graph sketch of any function (asymptotes, a sinusoid's amplitude and period marked), lines, circles, ellipses, hyperbolas, two lines crossing, the unit circle, a box plot, a factor tree, fraction bars, the complex plane.
• Δ on part of what you typed: put the cursor in the denominator and press prgm: the card is about that part. Δ also works on any line of the history.
• Word problems answer in words: "width w = 5 cm, length l = 13 cm" (type 36_cm in a box).
• Checked against 1,698 problems before release, 461 of them word problems: all right.
• Faster: the app is 29 KB smaller and 1–6% quicker.

New in 2.2.1

Word problems, laid out	A whole story on one line

• Find the right problem at a glance. more → 7: five tabs (% & rate, geometry, multivar, functions, recent), each problem shown as the sentence you'll fill in, with an example.
• 71 word problems, 22 new: sales tax, percent change, half-life, the score you need, law of cosines, angle of elevation, sectors, trapezoids, ages, coins and tickets, mixtures, limits…
• Combine them with commas. "[l] is [3] more than [2w], a rectangle [l] by [w] has perimeter [36], find [w]" on one line: w = 5, l = 13. Phrases nest, too.

New in 2.2

The Δ key	The answer bar

• Δ: "what is this?" Type anything, press prgm. DeltaCE names it and lists what a textbook would ask: a parabola's vertex, a circle's center, a sine wave's period, a number line for an inequality.
• Word problems in plain words. Type "[l] is [3] more than [2w]", then "a rectangle [l] by [w] has perimeter [36]", then "find [w]": w = 5, l = 13.
• One-row answer bar. ◀ ▶ flip an answer between its forms (factored, expanded, decimal); prgm shows what to do next.
• Cleaner answers. Rationalized denominators, physical constants that give their values, and a stack of bugs fixed. All the details.

What it does

• The Δ key. prgm on anything you type, or on the last answer: what it is and its facts, by kind (functions, equations, inequalities, conics, numbers, data, matrices, systems), with the next moves on 1 to 9. Typed while an answer shows, it also checks your answer against it.
• Word problems. more → Word problems: each one shown as its sentence, in five tabs on F1-F5 (% & rate, geometry, multivar, functions, recent); type a word to search them all. Fill the boxes with ▶; a story takes a fact a line (or all on one line, between commas), then "find". A comma right after a number keeps it in its box as a list (15 % of [80, 90]: both answers); ▶ out of the phrase, then a comma, starts the next phrase.
• The steps. After an answer, press enter to see how to get it, the way a worked example in a textbook does: derivatives, integrals, limits, sums and Taylor series (FlowCE Steps), and in algebra, linear and quadratic equations (always by the formula: a, b and c, the discriminant, the roots simplified), rational and radical equations (excluded values, the LCD, every candidate checked), factoring (GCF, differences of squares and cubes, two numbers or the ac method, grouping, rational roots), equations of degree 3 and 4 (factored, or as a quadratic in form: u = x² + 6x), systems of 2 or 3 equations by elimination, exponential and log equations (the same base, ln of both sides, the log rules, every solution checked), trig equations (the reference angle, its quadrants, every solution, those in [0, 2π)), implicit differentiation (implicitdiff(x^2+y^2=25,x,y)), polynomial division (long division, synthetic division, or factor and cancel with the excluded values: F4 on the steps page switches), inequalities (linear ones flip the sign by a negative; polynomial and rational ones get their critical numbers and a number tested in each interval) and absolute values (two cases or one compound inequality, every candidate checked; |A| = |B| too). Each step names its rule; ▲ ▼ move between them. An equation or inequality typed alone (3x-5<7) is solved.
• Answers like your textbook, and their other forms. F4 cycles an answer's forms: simplified, one fraction, factored, expanded, the completed square, long division, partial fractions, decimal; enter on one shows its work. On an antiderivative, F4 checks it by differentiating.
• The answer bar. Under an answer, one row: ◀ ▶ flip it through its forms (as F4 does), then prgm with the moves it offers (Factor · Zeros, or Derivative · Graph): prgm opens the answer's facts card with its moves numbered, 1 to 9 do one, More actions lists them all. Digits still start a new calculation and enter still shows the steps.
• A graph screen that knows its key points. Zeros, extrema, inflection points and crossings, exact ((π/3, √3/2)), labeled on the graph. Pan and zoom while a key is held, trace, a table, the tangent line, the area under the curve, value at x, solve f(x) = …, max and min on [a, b]. Equations in x and y (circles, ellipses, hyperbolas, tilted conics), parametric and polar curves, slope fields with solutions through points.
• Statistics and regression. more → Statistics: your data in two columns (the lists L1 and L2, shared with the console). A column's statistics with its box plot: mean, sum, sample and population standard deviation, min, Q1, median, Q3, max (the quartiles the TI's way). A curve fitted to the points (linear, quadratic, cubic, exponential, power, logarithmic) in exact form when it can be (y = 33/7 x + 324/7) with r and r², a predicted y, and the points with the curve on the graph screen, traced point by point. mean(L1), linear_regression(L1,L2) and the others work in the console too.
• Probability and inference. more → Probability: the normal, t, chi-square, binomial and Poisson distributions drawn with the area you ask for shaded, P(a ≤ X ≤ b), a tail or P(X = k), and the inverse (the x for an area, left, right or in the middle). Intervals and tests for a proportion (z) and a mean (t, its data from L1 if you like), on their curve, with the p-value.
• Function analysis. analyze(f) (or F2 → Analyze f(x)): domain, intercepts, symmetry, asymptotes and holes, increasing and decreasing, extrema, concavity, inflection points.
• Units. A units menu on alpha F4: 72 units in 8 categories, Celsius to Fahrenheit, results written as textbooks write them (96.5606 km/h, 120 min).
• Calculus 1, 2 and 3. Trig integrals, trig substitution, partial fractions, arc length, improper integrals that say diverges, limits that say does not exist, series and power series, differential equations with initial values, parametric and polar areas, gradients, multiple integrals, complex numbers, vectors, matrices.
• Type math as it looks. Fractions, powers, roots, integrals, sums, limits and derivatives are drawn in 2D as you type; commands come with a box for each argument and a line saying what they do. ▲ walks through your past calculations, ▼ searches every command.
• Keys that work like a TI's. (-) is a minus sign and 2nd (-) is Ans; starting a line with ×, ÷, +, − or ^ works on the last answer; 2nd enter brings back your last input; sto→ stores.
• Paper and Night themes, with DeltaCE's teal.
• Tested on the calculator itself. Before a release, Calc 1–3 and algebra problem lists and a 220-input class session run on an emulated TI-84 Plus CE, every answer checked against a computer's, along with out-of-memory and long-session tests. A long calculation shows Calculating; ON stops it.

Screenshots

prgm: what is it?	an inequality, on a number line	a word problem, in words
steps: a quadratic, by the formula	steps: factoring	steps: integration by parts
the answer bar: ◀ ▶ forms, prgm next	key points, exact	analyze(f)
equations in x and y	polar curves	slope fields
probability: a tail, shaded	a t test on its curve	more → Things to do
steps: a system	steps: a log equation	steps: a trig equation
steps: synthetic division (F4)	steps: an inequality	steps: an absolute value
statistics: your data	a column's statistics	a fitted line, exact
parametric curves	units	Σ 1/n² = π²/6
steps: a limit	steps: a sum	steps: a Taylor polynomial
type it as it looks	F4: other forms	a table of values
history	command search	Night theme

Install

The easy way: the DeltaCE page. Open it in Chrome or Edge with the calculator plugged in and click Install: it checks the calculator, erases its archive (after you agree), sends DeltaCE and opens the installer. Press enter once on the calculator: it installs and restarts by itself. On Windows it needs TI Connect CE 6.1 or newer installed (for its USB driver).

You need a TI-84 Plus CE (or TI-83 Premium CE) on OS 5.3 to 5.8.4. DeltaCE fills most of the memory (about 2.7 MB), so installing it erases the calculator's apps and archived files: back up anything you want to keep first. DeltaCE is a computer algebra system: follow your class and test rules (some tests, like the ACT, don't allow one).

By hand, with TI Connect CE:

1. Clear the memory: 2nd + (MEM) → 7:Reset... → right arrow twice to ALL → 1:All Memory... → 2:Reset.
2. Send the bundle: download DeltaCE.b84, drag it onto the calculator in TI Connect CE and send it.
3. Run the installer: prgm → enter → enter opens the arTIfiCE shell; enter starts INST and enter again installs. It counts down to 0; don't touch the calculator.
4. At "Success! Will now reset", press enter (a few times if the screen looks odd).
5. Start: clear, then apps → DeltaCE.

1. Clear the memory	3. Run the installer	5. Start DeltaCE

The bundle's INST is patched to run on OS 5.8.4 (the original stops with "Unknown OS version").

If something goes wrong

• The screen freezes at "Success! Will now reset": press the reset button on the back of the calculator (a pen tip or a paperclip). DeltaCE stays installed.
• The calculator acts strangely (menus glitch, TI Connect CE stays on "refreshing"): clear the RAM: 2nd + (MEM) → 7:Reset... → 1:All RAM... → 2:Reset. This does not remove DeltaCE.
• The calculator stays unresponsive: hold the reset button for a few seconds.

Keys

Key	What it does
F1 to F5	menus: algebra, calculus, trig, symbols, more (with 2nd or alpha: more menus)
prgm	Δ: what the line (or the last answer) is, its facts; 1 to 9 the next moves, enter the first
more → Word problems	the phrases, as sentences: F1-F5 their tabs, letters search; enter puts one on the line, ▶ goes to its next box
enter after an answer	its steps (calculus, equations, inequalities, factoring, divisions, F4's forms)
F4 on the steps page	another method, when there is one (a division: long, synthetic, factor and cancel)
◀ ▶ after an answer	its other forms, back and forth (as F4)
math	templates: fraction, root, integrals, derivative, limit, sum
▲ / ▼	history / search every command
F4 on an answer	its other forms
alpha F4	units
(-)	a minus sign; 2nd (-) is the last answer (Ans)
+ − × ÷ ^ x² first	works on the last answer, as on a TI (× 2 is Ans·2)
2nd enter	the last input again (ENTRY); press again for the one before
sto→	stores a value: 5 → b
ON while computing	stops the calculation
more → Graph	graphs the line or the answer: F1 pan or trace, F2 zoom, F3 key points and tools, F4 table, F5 more
more → Statistics	data in L1 and L2: F1/F2 a column's statistics, F3 fit a curve, F4 plot the points, F5 edit (insert, delete, sort, clear)
more → Probability	a distribution: F1 which one, F2 the region, F3 inverse, F4 intervals and tests; type the values, ◀ ▶ move
mode	settings (Simplify answers on or off), shortcuts, about
2nd quit	quit (your session is kept)

Building

DeltaCE is built on macOS with the CE C/C++ toolchain v15 (steps-units: make APPLANG=en STEPS=1 UNITS=1, linked as an application), packed by app_tools/pack_app.py and cut into 41-42 AppIns pieces by app_tools/make_segments.py. Clone with --recursive: the math engine is the src/giac submodule, a fork of FlowCE's with fixes for the calculator's 24-bit int. layout.ld places the code in flash for the flash cache (made from emulator traces of training sessions); a build of other code ignores it. The app must fit in 2,818,045 bytes; INST stops on a last piece under 1 KB, so such a build is padded.

tools/emu/ drives the CEmu emulator for the regression tests, the screenshots and the GIFs above (it needs your own calculator's ROM dump, which is never shared), tools/hostgiac/ builds the same engine on a computer to compare answers, and tests/host/ holds host tests of the editor and the 2D layout.

Credits and license

DeltaCE, by Gabriel, is a fork of FlowCE by Tommy Bell, which is a fork of KhiCAS by Bernard Parisse.

• Math engine: Giac, by Bernard Parisse and contributors (Institut Fourier, Université Grenoble Alpes).
• Interface, steps, the web installer and 2.2's quicker menus: FlowCE, by Tommy Bell.
• Console interface: adapted from Eigenmath for the Casio Prizm by G. Maia, Mike Smith, Nemhardy and LePhenixNoir.
• Thanks to Adrien Bertrand, Xavier Andreani and the TI-83/84 development community, especially Jacob Young, commandblockguy and Matt Waltz.
• Installer: arTIfiCE by YvanTT.
• Fonts: Atkinson Hyperlegible (Braille Institute) and STIX Two, under the SIL Open Font License (tools/fonts/src).

DeltaCE is free software under the GNU General Public License, version 3 or later. It comes with no warranty. Not affiliated with Texas Instruments; TI-84 Plus CE is a trademark of Texas Instruments.